Portable data medium with integrated memories is used for various purposes, for example for storing personal medical data or for storing amounts of money. The danger exists that if the data medium is lost or stolen, data or, respectively, amounts of money, are irretrievably lost to the legitimate user. In order to secure these data for the user, it is suggested with the invention to use a small terminal in addition to the data medium, with which the data medium can be connected and wherein subsequently data are copied from the data medium to the terminal. Such terminal is for example necessary in any event for specific types of data media for the operation and for displaying amounts of money. If the data medium is lost, in this case the data can be recovered from the terminal.